Integral Equation Failure in Wave Calculations

Abstract
Over the past few years increasing attention has been given to the development of diffraction theories of water wave scattering. These theories take into account the scattering of waves by large submerged or semi submerged objects, as well as effects of both free surface and bottom. The purpose of the present paper is to show that there may be characteristic wavelengths for which the potential theory formulation breaks down, and the solution of the boundary value problem cannot be represented by a wave source integral formula.

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